Computing eigenvalues occurring in continuation methods with the Jacobi-Davidson QZ method (Q1383040)

The paper is concerned with the computation of stationary solutions of a differential system, involving one or more physical parameters, using a technique called ``continuation method''. In order to determine whether a stationary solution is stable and to find the bifurcation points of the system, the rightmost eigenvalues of a related generalized eigenvalue problem are computed. The QZ method of Jacobi-Davidson, recently developed [SIAM J. Sci. Comput., to appear, or Preprint No. 941 Dept. Math., Utrecht Univ., Netherland] is used for computing the eigenvalues. As an application, the 2D Rayleigh-Bernard problem is considered. Numerical examples are performed for illustrate the performance of the Jacobi-Davidson QZ method.